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In this paper, an in-depth theoretical study on some physical properties of Ti_0.5Ta_0.5 alloy with systematic symmetry under high pressure is conducted via first-principles calculations, and relevant physical parameters are calculated. The results demonstrate that the calculated parameters, including lattice parameter, elastic constants, and elastic moduli, fit well with available theoretical and experimental data when the Ti_0.5Ta_0.5 alloy is under <inline-formula> <math display="inline"> <semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>, indicating that the theoretical analysis method can effectively predict the physical properties of the Ti_0.5Ta_0.5 alloy. The microstructure and macroscopic physical properties of the alloy cannot be destroyed as the applied pressure ranges from 0 to 50GPa, but the phase transition of crystal structure may occur in the Ti_0.5Ta_0.5 alloy if the applied pressure continues to increase according to the TDOS curves and charge density diagram. The value of Young’s and shear modulus is maximized at <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mo>=</mo> <mn>25</mn> <mtext> </mtext> <mi>GPa</mi> </mrow> </semantics> </math> </inline-formula>. The anisotropy factors <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>A</mi> <mrow> <mrow> <mo>(</mo> <mrow> <mn>100</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>[</mo> <mrow> <mn>001</mn> </mrow> <mo>]</mo> </mrow> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>A</mi> <mrow> <mrow> <mo>(</mo> <mrow> <mn>110</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>[</mo> <mrow> <mn>001</mn> </mrow> <mo>]</mo> </mrow> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> are equal to 1, suggesting the Ti_0.5Ta_0.5 alloy is an isotropic material at 28 GPa, and the metallic bond is strengthened under high pressure. The present results provide helpful insights into the physical properties of Ti_0.5Ta_0.5 alloy.